To find the reference angle for \( \frac{8\pi}{5} \), follow these steps:

1. **Identify the quadrant**: 
   Since \( \frac{8\pi}{5} \) is greater than \( \pi \) (which equals \( \frac{5\pi}{5} \)) but less than \( 2\pi \) (which equals \( \frac{10\pi}{5} \)), the angle lies in the **third quadrant**.

2. **Find the reference angle**:
   The reference angle in the third quadrant is found by subtracting \( \pi \) (or \( \frac{5\pi}{5} \)) from \( \frac{8\pi}{5} \):
   \[
   \text{Reference angle} = \frac{8\pi}{5} - \pi = \frac{8\pi}{5} - \frac{5\pi}{5} = \frac{3\pi}{5}
   \]

So, the reference angle is \( \frac{3\pi}{5} \).

Would you like further details or have any questions about this process?

Here are five related questions to explore further:
1. What is the reference angle for \( \frac{9\pi}{4} \)?
2. How do you calculate reference angles in the fourth quadrant?
3. Can you determine the reference angle for \( 330^\circ \)?
4. What are the reference angles for negative angles?
5. How do reference angles relate to trigonometric function values?

**Tip**: Reference angles are always positive and lie between \( 0 \) and \( \frac{\pi}{2} \) (or between 0° and 90° in degrees).

Learn how to find the reference angle for the radian measure 8π/5. This step-by-step guide walks through identifying the angle's quadrant, applying the reference angle formula, and understanding key trigonometric concepts. Suitable for high school students in Grades 10-12.

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